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动画演示几何与数据分析

动画演示几何与数据分析
几何画板及绘图内容加载中，请稍等……
2017-03-25 00:36
圆角矩阵最值优化几何作图
①本范例通过动画演示圆、角、多边形等几何图形的动态变化与数据分析；②涉及核心数学概念包括角度、圆、全等、内切圆、饼图、线性规划、矩阵、线性回归；③作图要点运用了Circle（圆）、Point（点）、Segment（线段）、Intersect（交点）、Midpoint（中点）、CircleArc（圆弧）、Min（最小值）、CircleSector（扇形）、Dilate（缩放）、Rotate（旋转）、Vector（向量）、Translate（平移）、Line（直线）、Angle（角度）等GeoGebra命令与对象；④适合高中及以上学段，用于几何作图、数据分析及算法可视化教学。

GeoGebra 命令及参数

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Point(c) → D
  4. Segment(C, D) → f
  5. Point(c) → I
  6. Circle(I, f) → k
  7. Intersect(c, k, 2) → J
  8. Segment(I, J) → i
  9. Midpoint(f) → K
  10. Midpoint(i) → N
  11. CircleArc(A, I, C) → d
  12. Point(d) → E
  13. Circle(E, f) → e
  14. Intersect(d, e, 2) → F
  15. Segment(E, F) → g
  16. CircleArc(A, I, E) → h
  17. Point(h) → G
  18. Circle(G, f) → p
  19. Intersect(c, p, 2) → H
  20. Segment(G, H) → j
  21. Midpoint(g) → L
  22. Midpoint(j) → M
  23. Segment(M, L) → l
  24. Segment(M, K) → m
  25. Segment(N, L) → n
  26. Segment(N, K) → q
  27. Min({l, n, m, q}) → a
  28. Circle(M, (0.2 * a)) → r
  29. Intersect(r, l, 1) → O
  30. Intersect(r, m, 1) → P
  31. CircleSector(M, O, P) → s
  32. Dilate(C, If[0 < b ≤ 1, 1 - b, 0], K) → C'
  33. Segment(C, C') → t
  34. Dilate(K, If[1 < b ≤ 2, 2 - b, 0], D) → K'
  35. Segment(K, K') → f_1
  36. Rotate(C, If[2 < b ≤ 3, ((b - 2) * π), π], K) → C'_1
  37. Rotate(C', If[2 < b ≤ 3, ((b - 2) * π), π], K) → C''
  38. Segment(C'_1, C'') → t'
  39. Dilate(E, If[3 < b ≤ 4, 4 - b, 0], L) → E'
  40. Dilate(G, If[3 < b ≤ 4, 4 - b, 0], M) → G'
  41. Dilate(I, If[3 < b ≤ 4, 4 - b, 0], N) → I'
  42. Segment(E, E') → g_1
  43. Segment(G, G') → h_1
  44. Segment(I, I') → i_1
  45. Dilate(M, If[4 < b ≤ 5, 5 - b, 0], H) → M'
  46. Dilate(N, If[4 < b ≤ 5, 5 - b, 0], J) → N'
  47. Dilate(L, If[4 < b ≤ 5, 5 - b, 0], F) → L'
  48. Segment(L, L') → j_1
  49. Segment(M, M') → k_1
  50. Segment(N, N') → l_1
  51. Dilate(C, If[5 < b ≤ 6, 6 - b, 0], J) → C'_2
  52. Dilate(C, If[5 < b ≤ 6, 6 - b, 0], H) → C'_3
  53. Dilate(C, If[5 < b ≤ 6, 6 - b, 0], F) → C'_4
  54. Vector(C, C'_2) → u
  55. Vector(C, C'_3) → v
  56. Vector(C, C'_4) → w
  57. Translate(C, w) → C'_5
  58. Translate(C', w) → C''_1
  59. Segment(C'_5, C''_1) → t'_1
  60. Translate(C, v) → C'_6
  61. Translate(C', v) → C''_2
  62. Segment(C'_6, C''_2) → t'_2
  63. Translate(C, u) → C'_7
  64. Translate(C', u) → C''_3
  65. Segment(C'_7, C''_3) → t'_3
  66. Line(J, t) → m_1
  67. Line(F, t) → n_1
  68. Line(H, t) → p_1
  69. Point(m_1) → Q
  70. Angle(N, J, Q) → α
  71. Point(p_1) → R
  72. Point(n_1) → S
  73. Angle(S, F, L) → β
  74. Angle(R, H, G) → γ
  75. Rotate(C'_7, If[6 < b ≤ 7, ((-(b - 6)) * α), (-α)], J) → T
  76. Rotate(C''_3, If[6 < b ≤ 7, ((-(b - 6)) * α), (-α)], J) → U
  77. Segment(T, U) → q_1
  78. Rotate(C'_5, If[6 < b ≤ 7, ((b - 6) * β), β], F) → V
  79. Rotate(C''_1, If[6 < b ≤ 7, ((b - 6) * β), β], F) → W
  80. Segment(V, W) → r_1
  81. Rotate(C'_6, If[6 < b ≤ 7, ((b - 6) * γ), γ], H) → Z
  82. Rotate(C''_2, If[6 < b ≤ 7, ((b - 6) * γ), γ], H) → A_1
  83. Segment(Z, A_1) → s_1
  84. Rotate(T, If[7 < b ≤ 8, ((-(b - 7)) * π), (-π)], N) → T'
  85. Rotate(U, If[7 < b ≤ 8, ((b - 7) * π), π], N) → U'
  86. Segment(T', U') → t_1
  87. Rotate(V, If[7 < b ≤ 8, ((-(b - 7)) * π), (-π)], L) → V'
  88. Rotate(W, If[7 < b ≤ 8, ((b - 7) * π), π], L) → W'
  89. Segment(V', W') → a_1
  90. Rotate(Z, If[7 < b ≤ 8, ((-(b - 7)) * π), (-π)], M) → Z'
  91. Rotate(A_1, If[7 < b ≤ 8, ((b - 7) * π), π], M) → B_1
  92. Segment(Z', B_1) → b_1
  93. Dilate(M, If[8 < b ≤ 9, 9 - b, 0], L) → M'_1
  94. Dilate(N, If[8 < b ≤ 9, 9 - b, 0], K) → N'_2
  95. Segment(M, M'_1) → c_1
  96. Segment(N, N'_2) → f_2
  97. Dilate(M, If[8 < b ≤ 9, 9 - b, 0], K) → M'_2
  98. Segment(M, M'_2) → d_1
  99. Dilate(N, If[8 < b ≤ 9, 9 - b, 0], L) → N'_1
  100. Segment(N, N'_1) → e_1
  101. Angle(L, M, K) → δ
  102. Rotate(O, If[9 < b ≤ 10, ((b - 9) * δ), δ], M) → O'
  103. CircleSector(M, O, O') → c_2
  104. Dilate(M, If[10.5 < b ≤ 11.5, 11.5 - b, 0], N) → M'_3
  105. Vector(M, M'_3) → u_1
  106. Translate(s, u_1) → s'
  107. Line(N, d_1) → g_2
  108. Point(g_2) → C_1
  109. Angle(K, N, C_1) → ε
  110. Rotate(s', If[11.5 < b ≤ 12.5, ((b - 11.5) * ((2 * π) - ε)), (2 * π) - ε], N) → s''